var formats = new string[]
{
    "dd MMM yyyy",
    "dd MMM",
    "MMM yyyy",
    "MMM"
};

var monthEngl = new string[12];
var monthInLocal = new string[12];

for (int i = 1; i <= 12; i++)
{
    monthEngl[i - 1] = new CultureInfo("en").DateTimeFormat.GetMonthName(i).ToLower();
    monthInLocal[i - 1] = new CultureInfo("it").DateTimeFormat.GetMonthName(i).ToLower();
}

var split = query.ToLower().Trim().Split(' ', StringSplitOptions.RemoveEmptyEntries);

for (int i = 0; i < split.Length; i++)
{
    if (split[i].Length > 3)
    {
        for (int j = 0; j < 12; j++)
        {
            if (monthEngl[j].StartsWith(split[i]) || monthInLocal[j].StartsWith(split[i]))
            {
                split[i] = split[j].Substring(0, 3);
                break;
            }
        }
    }
}

var text = string.Join(' ', split);

foreach (var format in formats)
{
    if (TryParseExact(text, format, out DateTime result))
    {
        Console.Write("\nParsed: " + result.ToShortDateString());
        Console.SetCursorPosition(header.Length, 1);
        break;
    }